Fast sorting data to Lissajous Curve

Hi community. I am trying to ascertain the quickest way to sort data to a Lissajous pattern, as I want to perform this in real time.

My data consists of an array of values, lets call this variable data, and it contains 10,000 values.

I want to specify two properties of a sinewave (two different sinewaves, each with different periods). Call one of them X, and one of them Y. I want the X sinewave to map the X position and the Y value to map the Y position of a 512x512 grid, for example.

But I want this to happen fast and elegantly, I am currently just brute forcing it, which is slow.

Any suggestions?